Karttunen Semantics. Last week. LING 147. Semantics of Questions Week 4 Yimei Xiang September 22, I. Intensionality

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1 LING 147. Semantics of Questions Week 4 Yimei Xiang September 22, 2016 Last week I. Intensionality Karttunen Semantics The intension of an expression X is a function which applies to a possible world and returns the extension of X in that world. (1) a. X w ( the extension of X in w ) b. λw. X w ( the intension of X ) The intension of a sentence is a proposition: a function from worlds to truth values. The intension of a predicate of type xe, ty is a property: a function from worlds to xe, ty functions. The intension of a definite NP is an individual concept: a function from worlds to entities. The extension of a proper name or a logical expression (e.g., not, every) is not world-dependent. Propositions can also be viewed as the set of possible worlds where this proposition is true. Hence, we can use set-theoretical operations to represent the following relations and operations: Relations and operations p entails q p contradicts q p and q p or q p is possible p is necessary Set-theoretical notations p Ď q p X q p X q p Y q p p W Using intensions in semantic composition (2) Intensional Functional Application If {β, γ} is the set of α s daughters, β P D xxs,σy,τy, and γ P D σ, then α β pλw. γ w q Alternatively, we can assume that the predicate left carries an world variable w, which is then abstracted over by a λ-operator. (Percus 2000) (3) John believes that Mary left. John 1 believes xst,ety λw.left 1 wpmq λw left 1 wpmq Mary left w 1

2 II. Core assumptions of Hamblin Semantics A possible answer denotes a proposition. A short answer is an elliptical form of the corresponding full answer. A wh-item denotes a set of individuals. A question denotes a Hamblin set, namely, a set of possible answers. Hamblin sets are composed point-wise. (4) Point-wise Functional Application If α is of type xσ, τy and β is of type σ, then a. α Ď D xσ,τy b. β Ď D σ c. αpβq is of type τ, and αpβq tapbq a P α ^ b P β u (5) a. Mary came. b. Who came? tλw.came 1 wpmqu tλw.came 1 wpxq : human 1u Mary tmu came tλw.came 1 wpxqu who tx : human 1u came tλw.came 1 wpxqu (6) Is it the case that John left? tλw.left 1 wpjq, λw. left 1 wpjqu is it the case that tλp.p, λpλw. p w u tλw.left 1 wpjqu John left (7) Did JOHN come or MARY come? ALT-Q tλw.came 1 wpjq, λw.came 1 wpmqu tλw.came 1 wpjqu John came or λα xst,ty λβ xst,ty.α Y β tλw.came 1 wpmqu Mary came Plan for today Compare Hamblin and categorial Alternative Semantics of focus Karttunen Semantics 2

3 1 Compare Hamblin Semantics and traditional categorial approaches Discussion: Are the denotations of (8a-b) equivalent under Hamblin Semantics? What about under categorial approaches? [Recall that categorial approaches assume that questions denote lambda abstracts.] (8) a. Did JOHN come or MARY come? ALT-Q b. [Among John and Mary,] which person came? Discussion: Can we derive a Hamblin set based on a lambda abstract? What about retrieving a lambda abstract out of the corresponding Hamblin set? An inclusive comparison between categorial approaches and Hamblin Semantics Retrieving the question nucleus Getting short answers Getting full answers Uniform semantic type Question coordinations Type-driven wh-movement Categorial approaches Yes Yes Yes No No Yes Hamblin Semantics Although Hamblin Semantics treat questions uniformly as of type xst, ty, it still has imperfections in analyzing question coordinations. Conjunction is traditionally treated as set-intersection. (9) John left and Mary stayed John left X Mary stayed But, the conjunction of two questions cannot be the intersection of the Hamblin sets of the two questions: (10) who left and who stayed who left X who stayed H NO WAY! Hence, Hamblin Semantics has to define conjunction as pointwise intersection. 1 (11) Q 1 and Q 2 tp X q : p P Q 1 ^ q P Q 2 u 1 Inquisitive Semantics maintains the basic intersection semantics of conjunction by treating questions as sets of proposition sets. (See Ciardelli et al. 2016, Composing Alternatives ) 3

4 2 Alternatives Semantics of focus (Rooth 1992) Focus affects the suitability of a sentence as answer of the given question. Observe the prosodic dependence between questions and answers: (12) Who invited Bill? Core definitions a. JOHN invited Bill. b. # John invited BILL. (13) Every expression α has an ordinary value α 0 and a focus value α f. a. α 0 is simply the truth value of α (i.e., the one that we already know). b. α f is the set of all ordinary semantic values obtained by substituting alternatives for any F-marked subparts of α. Compute the focus value compositionally: (14) Terminal " nodes (TN) t α 0 u if α is not focused α if α is focused D typep α 0 q Pointwise Functional Application (PFA) αpβq f tapbq a P α f, b P β f u Exercise: Compute the focus value of the following sentences compositionally: (15) JOHN F invited Bill. S JOHN F invited Bill Use the Rooth-style terms to define Hamblin sets: (16) a. who 0 is undefined b. who f tx : human 1u c. [ TP who came] 0 is undefined d. [ TP who came] f tλw.came 1 wpxq : human 1u e. C r`whs [TP] 0 TP f (Beck & Kim 2006, see also Shimoyama 2001) (interrogative C 0 returns the focus-semantic value of TP as the ordinary semantic value of CP.) Due to Principle of Interpretability, we cannot say that the ordinary value of a question is undefined. (17) Principle of Interpretability (Beck 2006: p. 16) An LF must have an ordinary semantic value. 4

5 Exercise: Use the following toy LF to derive the Hamblin set for Who does John like?. (18) CP C TP John invited who Explain the prosodic dependence between questions and answers: (19) Question-Answer Congruence (Rooth 1992: 86) A sentence S is a possible answer of a question Q iff Q 0 Ď S f (20) a. who invited Bill? 0 Ď JOHN F invited Bill f b. Did JOHN or MARY invited Bill? 0 Ď JOHN F invited Bill f 3 Karttunen Semantics 3.1 Core assumptions of Karttunen (1977) The denotation of a question is the set of true answers (called Karttunen set ). Indirect questions that use a non-factive interrogative-embedding predicate (e.g., tell, predict) take veridical readings. This contrast suggests that the veridicality of tell in (21b) comes from the embedded question. 2 (22) a. John told us that Mary left. ù Mary left. b. John told us who left. ù For some true answer p as to who came, John told us p. Wh-words are existentially quantified noun phrases. Composition (Using PTQ by Montague) [Don t worry if you don t understand this part...] A proto-question rule shifts the meaning of declarative sentence from a proposition to a protoquestion, namely, the a set of true propositions that are identical to this proposition. The wh-item takes QR and quantifies into the proto-question, yielding a set of true answers. (23) By WH-quantification rule Question λp.dxrpeople pxq ^ ppwq 1 ^ p ˆcame1 pxqs who By λp.dxrpeople pxq ^ P txus Proto-question rule Proto-question tp : ppwq 1 ^ p ˆcame 1 pxqu Proposition ˆcame 1 pxq 2 In contrast, Spector & Egré (2015) show that declarative-embedding tell does admit a factive/veridical reading. (21) a. Sue told Jack that Fred is the culprit. ù Fred is the culprit. b. Sue didn t tell Jack that Fred is the culprit. ù Fred is the culprit. c. Did Sue tell Jack that Fred is the culprit? ù Fred is the culprit. 5

6 3.2 Transporting Karttunen Semantics into a GB-style LF Composing wh-questions (Heim 1995; a.o.) (24) Who came? xs, ty ANS w Q: xst, ty λp.dxrpeople pxq ^ p ˆcame1 pxqs λp t Dxrpeople pxq ^ p ˆcame1 pxqs who: xet, ty xe, λf.dxrpeople pxq ^ fpxqs ty λx.p ˆcame 1 pxq λx C 1 : t p ˆcame 1 pxq C 0 r`whs λq.p q ID λpλq.p q p: st IP: st ˆcame 1 pxq x came 1. The proto-question rule is ascribed to an identify (ID)-function at the C The wh-word is an existential quantifier; it undertakes QR to [Spec, CP] and quantifies into a predicate of identity relation. 3. Abstracting the first argument p of ID returns a Hamblin set, which is the question denotation. (25) Q λp.dxrpeople pxq ^ p ˆcame1 pxqs tˆcame 1 pxq : x P people $ u & ˆcame 1, pjq. ˆcame 1 pmq % ˆcame 1 - pj mq 4. An answerhood (ANS)-operator applies to the Hamblin set Q and the evaluation world w, returning the/a complete true answer in w. (Unlike Karttunen (1977), truth is introduced by the ANS-operator.) Many different ANS-operators have been proposed in the literature. (26) ANS Heim pqqpwq Ş tp : w P p P Qu (Heim 1994) (The conjunction of all the true answers) (27) ANS Dayal pqqpwq Dprw P p P Q P q P Q Ñ p Ď qss. ιprw P p P Q P q P Q Ñ p Ď qss (Dayal 1996) (The unique strongest true answer) 6

7 Compare Hamblin Semantics and Karttunen Semantics: Hamblin Karttunen (1977) Transformed Karttuen A declarative denotes A singleton set of propositions a proposition a proposition A question denotes a Hamblin set a Karttunen set a Hamblin set A wh-word denotes a set of individuals an D-quantifier an D-quantifier Composition rules point-wise FA etc. Montague PTQ FA, lambda calculus Exercise: Following (24), compose the Hamblin set for the single-pair reading of the following multi-wh question. (28) Who bought what? Composing polar-questions (29) Did John come? CP λprp ˆcame 1 pjq _ p ˆ came 1 pjqs : tˆcame 1 pjq, ˆ came 1 pjqu λp C 1.p ˆcame 1 pjq _ p ˆ came 1 pjq C 0 r`whs OP Y/N λpλqrp q _ p λw. q w s p IP ˆcame 1 pjq John came 7

8 Composing alternative-questions Recall that in Hamblin semantics, composing an alternative question has to use the type-shifted meaning of or (see (7)). We can avoid doing so using the ID-function. (Modified from Heim 2012) (30) Did JOHN come or MARY come? λprp ˆcame 1 pjq _ p ˆcame 1 pmqs : tˆcame 1 pjq, ˆcame 1 pmq} λp p ˆcame 1 pjq _ p ˆcame 1 pmq ID pˆcame 1 pjq p ˆcame 1 pjq John came or ID p ˆcame 1 pmq p ˆcame 1 pmq Mary came Discussion: In the alternative-question (31), can we treat John or Mary as a generalized quantifier as and derive the Hamblin set based on the following LF? (31) Did you see JOHN or MARY? ALT-Q CP DP J or M λx C1 C 0 r`whs IP ID p you saw x Heim (2012): only interrogative items can be moved to the spec of an interrogative C 0 r`whs. 8